In an investigation, $x$ represents temperature and $y$ represents the time taken for a reaction. The regression line of $y$ on $x$ passes through the mean point $(20,74)$ and has gradient $-\dfrac{3}{2}$.

A set of bivariate data has Pearson product-moment correlation coefficient $r=-0.08$. The observed values of $x$ satisfy $-3\leq x\leq 3$. A scatter diagram of the data shows points lying close to a curve shaped like a parabola.

For a set of bivariate data, the regression line of $y$ on $x$ is

and the regression line of $x$ on $y$ is

For a set of data, the regression line of $x$ on $y$ is

The regression line of $y$ on $x$ is

The observed values of $y$ satisfy $12\leq y\leq 30$.

For a set of bivariate data, the regression line of $y$ on $x$ is

and the regression line of $x$ on $y$ is

For a data set, the regression line of $y$ on $x$ is

and the regression line of $x$ on $y$ is

A scientist models the relationship between a variable $x$ and a positive variable $y$. The table gives values of $x$ and $\ln y$. The regression equation of $\ln y$ on $x$ is written as $\ln y=ax+b$.

A taxi company records the distance of a journey, $x$ km, and the fare, $y$ dollars, for five journeys. The data are shown in the table.

A sports scientist records the age, $x$, in decades, and sprint speed, $y$, in $\text{km}\,\text{h}^{-1}$, of five athletes. The data are shown in the table.

For a set of bivariate data, the regression line of $y$ on $x$ is $y=1.84x+12.5$ and Pearson's product-moment correlation coefficient is $r=0.912$. New variables $u$ and $v$ are defined by $u=x-5$ and $v=2y+10$.

A small museum recorded the number of days, $x$, after the opening of an exhibition and the number of visitors, $y$, on that day. A linear regression model for the data is

The mean of the recorded $x$-values is $8$, and there were $10$ recorded days.

A shop selling second-hand cameras records the age, $x$ years, and the repair cost, $y$ dollars, for six cameras. For these data,

A line of best fit drawn by eye must pass through the mean point. A student suggests the line $y=3x+1$.

A city council records the floor area, $x$, in hundreds of square metres, and the annual number of visits, $y$, in thousands, for several community libraries. For these data, Pearson's product-moment correlation coefficient is $r=0.84$. For this sample size, the critical value for testing linear correlation is $0.754$.

The regression line of $y$ on $x$ is

For a sample of adults, $x$ denotes the number of phone notifications received in one hour and $y$ denotes the number of minutes of uninterrupted reading in that hour. The regression line of $y$ on $x$ has gradient $-\frac{3}{2}$ and passes through the mean point $(12,54)$. The observed values of $x$ satisfy $4\leq x\leq 18$.

A craft workshop records the drying time, $x$ hours, and the percentage moisture remaining, $y$, for a set of clay tiles. A regression model for predicting $y$ from $x$ is

For these data, $r=-0.96$. For this sample size, the critical value for testing linear correlation is $0.878$.

For a set of bivariate data, the regression line of $x$ on $y$ is

The mean point of the data is $(10,9)$. The regression line of $y$ on $x$ has gradient $2$. A student rearranges the regression line of $x$ on $y$ to obtain $y=3x-21$ and uses this to predict $y$ from $x$.

A bicycle hire company records the number of sunshine hours, $x$, and the number of bicycles hired, $y$, on seven Saturdays. The paired data are
$(2,18),(4,35),(5,39),(7,54),(8,63),(10,76),(11,82)$

An events organiser records the rainfall, $x$ mm, and the attendance, $y$, at seven outdoor performances. The paired data are
$(0,510),(2,480),(5,430),(7,410),(9,360),(12,325),(14,290)$
For $n=7$, the critical value of $|r|$ at the $5\%$ significance level is $0.754$.

A city engineer records the traffic flow, $x$, in hundreds of vehicles per hour, and the noise level, $y$ dB, at six roads. The paired data are
$(12,55),(18,59),(21,61),(27,66),(33,71),(39,74)$

The table shows five paired observations of variables $x$ and $y$.

A marine biologist records the length, $x$ cm, and mass, $y$ g, of six fish. One observation appears to be unusual. The data are shown in the table.

The population $P$ of a bacterial culture, in thousands, is recorded at time $t$ hours. The table gives values of $t$ and $\ln P$. It is suggested that $P$ may be modelled by $P=Ae^{kt}$, where $A$ and $k$ are constants.

The table shows values of $x$ and $y$ for seven observations. The table suggests a curved relationship.

A museum records the age $x$ years of ceramic samples and their measured hardness $y$ on a standard scale. The regression line of $x$ on $y$ has gradient $0.03125$ and passes through the mean point. The mean age is $8.00$ years and the Pearson correlation coefficient is $0.750$.

A harbour officer records the time, $x$ hours after midnight, and the depth of water, $y$ metres, at six times during one tide cycle. The observations are

For a set of bivariate data, the regression line of $y$ on $x$ has equation

The regression line of $x$ on $y$ has equation